Numerical Modelling of Satellite Downlink Signals in a Finslerian-Perturbed Schwarzschild Spacetime

TL;DR

This paper develops a numerical method to analyze satellite signals in a Finslerian-perturbed Schwarzschild spacetime, aiming to test Finsler gravity theories through satellite observations and orbit modeling.

Contribution

It introduces a numerical approach to distinguish Finslerian effects from Schwarzschild perturbations in satellite signals, enhancing experimental tests of Finsler gravity.

Findings

Finslerian effects can be separated from Schwarzschild perturbations in highly eccentric orbits.

Numerical modeling can help identify Finslerian modifications in satellite signal data.

The method can distinguish gravitational effects from non-gravitational perturbations.

Abstract

The work presented in this paper aims to contribute to the problem of testing Finsler gravity theories by means of experiments and observations in the solar system. Within a class of spherically symmetric static Finsler spacetimes we consider a satellite with an on-board atomic clock, orbiting in the Finslerian-perturbed gravitational field of the earth, whose time signal is transmitted to a ground station, where its receive time and frequency are measured with respect to another atomic clock. This configuration is realized by the Galileo 5 and 6 satellites that have gone astray and are now on non-circular orbits. Our method consists in the numerical integration of the satellite's orbit, followed by an iterative procedure which provides the numerically integrated signals, i.e., null geodesics, from the satellite to the ground station. One of our main findings is that for orbits that are considerably more eccentric than the Galileo 5 and 6 satellite orbits, Finslerian effects can be separated from effects of perturbations of the Schwarzschild spacetime within the Lorentzian geometry. We also discuss the separation from effects of non-gravitational perturbations. This leads us to the conclusion that observations of this kind combined with appropriate numerical modelling can provide suitable tests of Finslerian modifications of general relativity.